PSU (power supply unit) or cable failure? I experienced a slightly similar problem when my scaleo p would freeze randomly at startup, then boot at other times (but never shut down as in your case). Try changing the PSU and see if there's any difference.
In my case, I juggled some of my RAM for a few minutes and, surprisingly, my scaleo p started working again. It may seem odd, but try to move (or remove) a couple of RAM cards.